Kinetic properties required for sustained or paradoxical control of metabolic fluxes under large changes in enzyme activities

The effect that an increase in the activity of an enzyme has on its flux normally decreases with activity increase. To achieve a large increase in flux by manipulating a single step would therefore require a high initial effect that maintains or increases when the activity is increased, what has been called sustained or paradoxical control. Using metabolic control analysis for large responses, we derive conditions for sustained or paradoxical control in terms of elasticity coefficients. These are used to characterise types of rate laws contributing to this behaviour. The result that simple pathways, with normal kinetics, subject to large activity changes can lead to paradoxical control behaviour suggests that this type of pattern may be much more ubiquitous than could have, in principle, been suspected.